Heat oil, add onion, carrots, and mushrooms, and sauté, stirring frequently, until onions are soft, about 5 minutes.
Meanwhile, prepare the spinach: if using fresh, wash, pat dry, de-stem (optional), and chop. If using frozen, thaw, drain, and squeeze out excess water. Stir in the ricotta, oregano, pepper, and a dash of salt.
Preheat oven to 350.
Spread about ½ c of sauce in bottom of the baking dish. Line with lasagna noodles, then spread about a third of the spinach mixture on the noodles, then add about a third of the vegetables. Add ½ c sauce, then another layer of noodles, then a third of the spinach and a third of the vegetables. Repeat once more, top with the rest of the sauce, and finish off with the mozzarella.
Cover with aluminum foil and bake for 50 minutes. Turn off oven, remove cover, and leave lasagna in warm oven for another 15 minutes, until set.